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On semilinear elliptic equations involving concave–convex nonlinearities and sign-changing weight function. (English) Zbl 1153.35036

The author studies the multiplicity results of positive solutions of the following elliptic equation:

-Δu=u p +λf(x)u q inΩ0uH 0 1 (Ω),(1)

where Ω is a bounded domain in N , 0<q<1<p<2 * ; 2 * =N+2 N-2 if N3, 2 * = if N=2, and f is a given function, λ>0. The author under suitable assumptions on the data (1) proves that (1) possesses at least two positive solutions for λ is sufficiently small.

35J60Nonlinear elliptic equations
35J20Second order elliptic equations, variational methods
35J25Second order elliptic equations, boundary value problems
47J30Variational methods (nonlinear operator equations)